International Journal of Physical Sciences
|
|
- Albert Carter
- 5 years ago
- Views:
Transcription
1 Vol. 9(4), pp , 28 February, 2014 DOI: /IJPS ISSN Copyright 2014 Author(s) retain the copyright of this article International Journal of Physical Sciences Full Length Research Paper Lehmann Type II weighted Weibull distribution N. I. Badmus 1 *, T. A. Bamiduro 2 and S. G. Ogunobi 3 1 Department of Statistics, Abraham Adesanya Polytechnic, Ijebu-Igbo, Nigeria. 2 Department of Mathematical Sciences, Redeemer's University, Redemption Camp, Ogun State, Nigeria. 3 Department of Science Laboratory Tehnology, Abraham Adesanya Polytechnic, Ijebu-Igbo, Nigeria. Accepted 5 February, 2014 We upgrade on the method used on weighted Weibull model proposed by Azzalini (1985) using the logit of Beta function by Jones (2004) to have Lehmann Type II weighted Weibull model with a view to obtaining a distribution that is more better than both weighted Weibull and Weibull distribution in terms of estimate of their characteristics and their parameter. The weighted Weibull distribution is proposed by slightly modifying the method of Azzalini (1985) on weighted distribution with additional shape and scale parameters. Some basic properties of the newly proposed distribution including moments and moment generating function, survival rate function, hazard rate function, asymptotic behaviours, and the estimation of parameters have been studied. Key words: Asymptotic, hazard rate, Lehmann Type II, moments, weighted-weibull. INTRODUCTION The Weibull distribution is a well known common distribution and has been a powerful probability distribution in reliability analysis, while weighted distributions are used to adjust the probabilities of the events as observed and recorded. The Weibull distribution can also be used as an alternative to Gamma and Log-normal distribution in reliability engineering and life testing. Numerous authors/researchers have been worked on Weibull and eponential distribution in literature. In a nut shell, Shahbaz et al. (2010) applied Azzalini s method with the Weibull distribution that produced a new class of weighted Weibull distribution in which they obtained the probability density and cumulative density function as given below:, > 0 (1) The graph of the probability density function of Equation (1) with is given Figure 1. In the literature, researchers/authors on Lehmann Type II are very few. Figure 1 is the pdf graph of the weighted Weibull by Shabarz (2010). The aim of this article is to introduce this distribution and study on its statistical properties. This article presents the proposed distribution Lehmann Type II weighted Weibull distribution. Thereafter, moments and moment generating function is studied. This is followed by a critical discussion of the estimation of parameters showing the empirical distribution of data and the study was concluded. (2) *Corresponding author. idowuolasunkanmi8169@yahoo.com Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License
2 weipdf Int. J. Phys. Sci. PDF of Weighted Weibull a=4,ß=3 Figure 1. The probability density function of weighted Weibull distribution with function from Equation (1) is given in Equation (2). and the cumulative density MATERIALS AND METHODS The proposed Lehmann Type Ii weighted Weibull distribution The logit of beta function (the link function of the beta generalized distribution) is introduced by Jones (2004), since then etensive work has been done using the logit of beta distribution in literature. For instance, Gupta and Kundu (1990) proposed a generalized eponential distribution that provides an alternative to eponential and Weibull distribution. Lee et al. (2007), Eugene and Famoye (2002) and Nadarajah and Kotz (2005) also used the logit of beta distribution and they provided an etension on eponential distribution. The logit of beta distribution used by Famoye and Olugbenga (2005) to introduce the Beta-Weibull distribution alongside its major properties. The transformation is called the Lehmann Type I distribution. There is a dual transformation defined by referred to as the Lehmann Type II distribution introduced by Cordeiro et al. (2011) among others. Figures 2, 3 and 4 shows pdf, cdf and hazard rate graphs at several values of parameters. Figure 2 clearly shows that it is rightly skewed, Figure 3 rise upward to right and Figure 4 shows the level at which the hazard rate by rightly upward breaking points. Now, let be a random variable form of the distribution with parameters and defined (1) and (2) using the logit of beta by Jones (2004), we then have (3) Both probability density and cumulative density function (pdf and cdf) of Lehmann Type II weighted Weibull distribution is obtained by substituting pdf and cdf of weighted Weibull distribution in Equations (1) and (2) into Equation (3) and set we then obtain (4) Where,. Equation (5) is the pdf of Lehmann Type II weighted Weibull distribution. setting (5) substituting into Equation (4), we get (6) (6)
3 LWWpdf LWWpdf LWWpdf Badmus et al. 73 The PDF of Lehmann Type II Weighted Weibull a=1, b=5,a=0.5,ß=2 The PDF of Lehmann Type II Weighted Weibull a=1,b=3,a=3,ß=4.5 The PDF of Lehmann Type II Weighted Weibull a=1,b=3,a=4,ß=3 Figure 2. The pdf of LWW distribution at various values of the parameters and it is clear that indeed it is rightly skewed. Figure 2 shows the pdf of LWW distribution at various values of the p clear that
4 LWWcdf LWWcdf LWWcdf Int. J. Phys. Sci. The CDF of Lehmann Type II Weighted Weibull b=3.5 The CDF of Lehmann Type II Weighted Weibull a=1,b=3,a=4,ß=2 The CDF of Lehmann Type II Weighted Weibull a=1,b=3,a=1,ß=1 Figure 3. The CDF of LWW with a=1, b=3, give the same pattern and shape.. However, at given various values of the parameters, the graphs
5 LWWhaz haz 0e+00 2e+05 4e+05 6e+05 8e+05 Badmus et al. 75 Hazard Rate of LWW a=1, b=0.5,a=1,ß=2 The Hazard Rate of LWW Distribution (b=1.8) Figure 4. The hazard rate function of Lehmann Type II weighted Weibull distribution with several values of the parameter. Therefore, Equation (4) can be re-written as From logit of beta link function, we show that Equation (7) equal to one (7) Figure 2 show the graph of the Lehmann Type II weighted Weibull distribution at different values of the parameters. Cumulative density function (CDF) We have defined the probability density function (pdf) of in Equation (6), then Equation (6) can be given as Then, recall that (8) and using the differential equation method on have Therefore, we and cdf is given as (9)
6 76 Int. J. Phys. Sci. The graph of cumulative distribution of Lehmann Type II Weighted Weibull is shown Figure 3. The survival rate function of the distribution which is investigated as follows. Now from Epression (4), we have The survival rate function of the is defined by taking the limit (10) The hazard rate function The hazard rate function of a random variable with the pdf and cdf is given by This shows that the asymptotic behaviours when, and it is sure that the distribution has at least a mode. = 0 However, with and respectively defined in Equations (4) and (9), the hazard rate function can be epressed as: or (11) Where W is the epression in Equation (5) To show that we get the following where, = MOMENTS AND MOMENT GENERATING FUNCTION Shittu and Adepoju (2013) described that when a random variable following a generalized beta generated distribution that is, is a constant and where is the inverse of CDF of the weighted Weibull distribution, since distribution is a special form when a=c=1.we then derive the moment generating function (mgf) of the proposed distribution and the general rth moment of a beta generated distribution is defined by (12) Also, using the taylor series epansion around the point to obtain (13) For simplification, we take the limit of the following: When Cordeiro et al. (2011) described an alternative series epansion in their paper for in terms of where k follows the parent distribution then for z = 0, 1, = 0, Equation (11) above tends to and equal to zero (Figure 4). Asymptotic behaviours Following the steps in Hazard Rate Function above, by taking the They further discussed another mgf of for generated beta distribution Where, Therefore, (14) (15)
7 Badmus et al. 77 Substituting both pdf and cdf (F() and f()) of the weighted Weibull distribution into Equation (15), we obtain We can also get the standard deviation (SD) as (23) (16) Others like coefficient of variation, skewness and kurtosis can easily be obtained. Equation (17) becomes the mgf of Lehmann Type II weighted Weibull distribution and by setting b=1 and i = 0, the same epression (17) is reduced to become the parent distribution. To obtain the rth moment of, the weighted Weibull distribution by Shahbaz et al. (2010) is given by (17) ESTIMATION OF PARAMETER The maimum likelihood estimate (MLEs) of the parameter of distribution following Cordeiro et al (2011) given the log-likelihood function for, where by setting. Shittu and Adepoju (2013) in their study discussed that to be a vector of parameter and given by (24) Equation (16) can be re-written as (18) Recall that, a = c = 1 (24) becomes (25) Moreover, the rth moment of the proposed distribution can also be written from the above equation (18) as given below: where, and (19) Again, setting b = 1 in Equation (19) leads to the rth moment of the weighted Weibull distribution by Shahbaz et al. (2010) and is given by While the rth moment of the proposed distribution is For determining the MLE of Equation (26) with respect to ( (26), we took the partial derivative of ) as follows: (27) (20) +(b- From Equation (20), one can easily obtain the mean about the origin e.g when r = 1and the second moment when r = 2, etc. The first moment of is obtain 1) (28) (21) +(b-1) The second moment can also be obtained as follows: (22) (29) where, The above equations can be solved using Newton Ralphson method to obtain the the MLE of ( ) respectively. Taking second derivatives of Equations 27, 28 and 29 with respect to the parameters above we can derive the interval estimate and hypothesis tests on the model parameter and inverse of fisher s information matri needed.
8 78 Int. J. Phys. Sci. RESULTS AND DISCUSSION Application to life time data set Here we used a data set studied by Shahbaz et al (2010) on life components in years to compare the Lehmann Type II weighted Weibull and weighted Weibull distribution. The data contains Life (Grouped data say (0 1.0, ,,> 5.0) and frequency all together is R software is used to determine the maimum likelihood estimates and the log-likelihood for the Lehmann Type II weighted Weibull distribution are: while the maimum likelihood estimates and the loglikelihood for the weighted Weibull distribution are: and, where denote log-likelihood of both Lehmann Type II weighted Weibull distribution and weighted Weibull distribution. The asymptotic covariance matri of the maimum likelihood estimates for the Lehmann Type II weighted Weibull distribution, which is generated from the inverse of fisher s information matri and is given by REFERENCES Azzalini A (1985). A class of distributions which include the normal ones, Scand. J. Stat. 12: Shahbaz S, Shahbaz MQ, Butt NZ (2010). A class of weighted Weibull distribution in Pakistan J. Statistics Operation Res. VI(1): Cordeiro GM, Aleandra C, Ortega MM, Edwin Sarabia JM (2011). Generalized Beta Generated distributions. ICMA Centre. Discussion Papers in Finance DP pp Gupta RD, Kundu D (1990). The role of weighted distribution in stochastic modeling. Communications in statistics, 19: Eugene NC, Famoye F (2002). Beta-Normal distribution and its applications. Communications in Statistics Theory and Methods 31: Famoye F, Lee C, Olugbenga O (2005). The beta-weibull distribution. J. Statistical Theory Applications, 4(2): Jones MC (2004). Families of distributions arising from distributions of order statistics test 13:1-43. Lee C, Famoye F, Olumolade O (2007). Beta-Weibull distribution: Some properties and applications to censored data. J. modern Appl. statistical methods, 6: Nadarajah S, Kotz S (2005). The beta eponential distribution. Reliability Eng. Syst. Safety, 91: Shittu OI, Adepoju AK (2013). On the Beta-Nakagami Distribution. Progress in Appl. Maths. 5(1): Following the result above, this shows that the new proposed distribution can take care even more skew data than the weighted Weibull distribution because of the additional shape parameter b, and with the hope that the model will be wider application to many areas of research e.g economics, finance, environmental, biomedical among others. Conclusion In a nut shell, we studied the statistical properties of the proposed distribution e.g moments, moment generating function, estimation of parameters with R software are presented in this paper. We also upgraded with an additional parameter to the eisting two parameters in the weighted Weibull distribution and with the method of maimum likelihood the parameters of the model were estimated in order to give way for the derivation of fisher information matri. The data used indicates that Lehmann Type II weighted Weibull distribution has a better representation of data and more fleible than weighted Weibull distribution. Conflict of Interests The author(s) have not declared any conflict of interests.
Some Statistical Properties of Exponentiated Weighted Weibull Distribution
Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 4 Issue 2 Version. Year 24 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals
More informationON THE SUM OF EXPONENTIALLY DISTRIBUTED RANDOM VARIABLES: A CONVOLUTION APPROACH
ON THE SUM OF EXPONENTIALLY DISTRIBUTED RANDOM VARIABLES: A CONVOLUTION APPROACH Oguntunde P.E 1 ; Odetunmibi O.A 2 ;and Adejumo, A. O 3. 1,2 Department of Mathematics, Covenant University, Ota, Ogun State,
More informationA Quasi Gamma Distribution
08; 3(4): 08-7 ISSN: 456-45 Maths 08; 3(4): 08-7 08 Stats & Maths www.mathsjournal.com Received: 05-03-08 Accepted: 06-04-08 Rama Shanker Department of Statistics, College of Science, Eritrea Institute
More informationExponential Pareto Distribution
Abstract Exponential Pareto Distribution Kareema Abed Al-Kadim *(1) Mohammad Abdalhussain Boshi (2) College of Education of Pure Sciences/ University of Babylon/ Hilla (1) *kareema kadim@yahoo.com (2)
More informationOn Five Parameter Beta Lomax Distribution
ISSN 1684-840 Journal of Statistics Volume 0, 01. pp. 10-118 On Five Parameter Beta Lomax Distribution Muhammad Rajab 1, Muhammad Aleem, Tahir Nawaz and Muhammad Daniyal 4 Abstract Lomax (1954) developed
More informationTopp-Leone Inverse Weibull Distribution: Theory and Application
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 10, No. 5, 2017, 1005-1022 ISSN 1307-5543 www.ejpam.com Published by New York Business Global Topp-Leone Inverse Weibull Distribution: Theory and Application
More informationFurther results involving Marshall Olkin log logistic distribution: reliability analysis, estimation of the parameter, and applications
DOI 1.1186/s464-16-27- RESEARCH Open Access Further results involving Marshall Olkin log logistic distribution: reliability analysis, estimation of the parameter, and applications Arwa M. Alshangiti *,
More informationGENERALISATION OF THE INVERSE EXPONENTIAL DISTRIBUTION: STATISTICAL PROPERTIES AND APPLICATIONS
GENERALISATION OF THE INVERSE EXPONENTIAL DISTRIBUTION: STATISTICAL PROPERTIES AND APPLICATIONS BY OGUNTUNDE, PELUMI EMMANUEL Matriculation Number: 13PCD00573 JUNE, 2017 GENERALISATION OF THE INVERSE EXPONENTIAL
More informationPROPERTIES AND DATA MODELLING APPLICATIONS OF THE KUMARASWAMY GENERALIZED MARSHALL-OLKIN-G FAMILY OF DISTRIBUTIONS
Journal of Data Science 605-620, DOI: 10.6339/JDS.201807_16(3.0009 PROPERTIES AND DATA MODELLING APPLICATIONS OF THE KUMARASWAMY GENERALIZED MARSHALL-OLKIN-G FAMILY OF DISTRIBUTIONS Subrata Chakraborty
More informationThe Inverse Weibull Inverse Exponential. Distribution with Application
International Journal of Contemporary Mathematical Sciences Vol. 14, 2019, no. 1, 17-30 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2019.913 The Inverse Weibull Inverse Exponential Distribution
More informationBeta-Linear Failure Rate Distribution and its Applications
JIRSS (2015) Vol. 14, No. 1, pp 89-105 Beta-Linear Failure Rate Distribution and its Applications A. A. Jafari, E. Mahmoudi Department of Statistics, Yazd University, Yazd, Iran. Abstract. We introduce
More informationTHE WEIBULL GENERALIZED FLEXIBLE WEIBULL EXTENSION DISTRIBUTION
Journal of Data Science 14(2016), 453-478 THE WEIBULL GENERALIZED FLEXIBLE WEIBULL EXTENSION DISTRIBUTION Abdelfattah Mustafa, Beih S. El-Desouky, Shamsan AL-Garash Department of Mathematics, Faculty of
More informationA NEW WEIBULL-G FAMILY OF DISTRIBUTIONS
A NEW WEIBULL-G FAMILY OF DISTRIBUTIONS M.H.Tahir, M. Zubair, M. Mansoor, Gauss M. Cordeiro, Morad Alizadeh and G. G. Hamedani Abstract Statistical analysis of lifetime data is an important topic in reliability
More informationResearch Article On a Power Transformation of Half-Logistic Distribution
Probability and Statistics Volume 016, Article ID 08436, 10 pages http://d.doi.org/10.1155/016/08436 Research Article On a Power Transformation of Half-Logistic Distribution S. D. Krishnarani Department
More informationA THREE-PARAMETER WEIGHTED LINDLEY DISTRIBUTION AND ITS APPLICATIONS TO MODEL SURVIVAL TIME
STATISTICS IN TRANSITION new series, June 07 Vol. 8, No., pp. 9 30, DOI: 0.307/stattrans-06-07 A THREE-PARAMETER WEIGHTED LINDLEY DISTRIBUTION AND ITS APPLICATIONS TO MODEL SURVIVAL TIME Rama Shanker,
More informationTwo Weighted Distributions Generated by Exponential Distribution
Journal of Mathematical Extension Vol. 9, No. 1, (2015), 1-12 ISSN: 1735-8299 URL: http://www.ijmex.com Two Weighted Distributions Generated by Exponential Distribution A. Mahdavi Vali-e-Asr University
More informationThe Kumaraswamy-Burr Type III Distribution: Properties and Estimation
British Journal of Mathematics & Computer Science 14(2): 1-21, 2016, Article no.bjmcs.19958 ISSN: 2231-0851 SCIENCEDOMAIN international www.sciencedomain.org The Kumaraswamy-Burr Type III Distribution:
More informationWEIBULL BURR X DISTRIBUTION PROPERTIES AND APPLICATION
Pak. J. Statist. 2017 Vol. 335, 315-336 WEIBULL BURR X DISTRIBUTION PROPERTIES AND APPLICATION Noor A. Ibrahim 1,2, Mundher A. Khaleel 1,3, Faton Merovci 4 Adem Kilicman 1 and Mahendran Shitan 1,2 1 Department
More informationLogistic-Modified Weibull Distribution and Parameter Estimation
International Journal of Contemporary Mathematical Sciences Vol. 13, 2018, no. 1, 11-23 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2018.71135 Logistic-Modified Weibull Distribution and
More informationAn Extended Weighted Exponential Distribution
Journal of Modern Applied Statistical Methods Volume 16 Issue 1 Article 17 5-1-017 An Extended Weighted Exponential Distribution Abbas Mahdavi Department of Statistics, Faculty of Mathematical Sciences,
More informationINVERTED KUMARASWAMY DISTRIBUTION: PROPERTIES AND ESTIMATION
Pak. J. Statist. 2017 Vol. 33(1), 37-61 INVERTED KUMARASWAMY DISTRIBUTION: PROPERTIES AND ESTIMATION A. M. Abd AL-Fattah, A.A. EL-Helbawy G.R. AL-Dayian Statistics Department, Faculty of Commerce, AL-Azhar
More informationA New Family of Distributions: Libby-Novick Beta
International Journal of Statistics and Probability; Vol. 3, No. 2; 214 ISSN 1927-732 E-ISSN 1927-74 Published by Canadian Center of Science and Education A New Family of Distributions: Libby-Novick Beta
More informationA Marshall-Olkin Gamma Distribution and Process
CHAPTER 3 A Marshall-Olkin Gamma Distribution and Process 3.1 Introduction Gamma distribution is a widely used distribution in many fields such as lifetime data analysis, reliability, hydrology, medicine,
More informationTHE BETA WEIBULL-G FAMILY OF DISTRIBUTIONS: THEORY, CHARACTERIZATIONS AND APPLICATIONS
Pak. J. Statist. 2017 Vol. 33(2), 95-116 THE BETA WEIBULL-G FAMILY OF DISTRIBUTIONS: THEORY, CHARACTERIZATIONS AND APPLICATIONS Haitham M. Yousof 1, Mahdi Rasekhi 2, Ahmed Z. Afify 1, Indranil Ghosh 3,
More informationProperties a Special Case of Weighted Distribution.
Applied Mathematics, 017, 8, 808-819 http://www.scirp.org/journal/am ISSN Online: 15-79 ISSN Print: 15-785 Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution Arooj
More informationThe Odd Exponentiated Half-Logistic-G Family: Properties, Characterizations and Applications
Chilean Journal of Statistics Vol 8, No 2, September 2017, 65-91 The Odd Eponentiated Half-Logistic-G Family: Properties, Characterizations and Applications Ahmed Z Afify 1, Emrah Altun 2,, Morad Alizadeh
More informationThe Marshall-Olkin Flexible Weibull Extension Distribution
The Marshall-Olkin Flexible Weibull Extension Distribution Abdelfattah Mustafa, B. S. El-Desouky and Shamsan AL-Garash arxiv:169.8997v1 math.st] 25 Sep 216 Department of Mathematics, Faculty of Science,
More informationTransmuted Exponentiated Gumbel Distribution (TEGD) and its Application to Water Quality Data
Transmuted Exponentiated Gumbel Distribution (TEGD) and its Application to Water Quality Data Deepshikha Deka Department of Statistics North Eastern Hill University, Shillong, India deepshikha.deka11@gmail.com
More informationOn the Comparison of Fisher Information of the Weibull and GE Distributions
On the Comparison of Fisher Information of the Weibull and GE Distributions Rameshwar D. Gupta Debasis Kundu Abstract In this paper we consider the Fisher information matrices of the generalized exponential
More informationThe Compound Family of Generalized Inverse Weibull Power Series Distributions
British Journal of Applied Science & Technology 14(3): 1-18 2016 Article no.bjast.23215 ISSN: 2231-0843 NLM ID: 101664541 SCIENCEDOMAIN international www.sciencedomain.org The Compound Family of Generalized
More informationThe Gamma Generalized Pareto Distribution with Applications in Survival Analysis
International Journal of Statistics and Probability; Vol. 6, No. 3; May 217 ISSN 1927-732 E-ISSN 1927-74 Published by Canadian Center of Science and Education The Gamma Generalized Pareto Distribution
More informationA New Method for Generating Distributions with an Application to Exponential Distribution
A New Method for Generating Distributions with an Application to Exponential Distribution Abbas Mahdavi & Debasis Kundu Abstract Anewmethodhasbeenproposedtointroduceanextraparametertoafamilyofdistributions
More informationMoments of the Reliability, R = P(Y<X), As a Random Variable
International Journal of Computational Engineering Research Vol, 03 Issue, 8 Moments of the Reliability, R = P(Y
More informationMARSHALL-OLKIN EXTENDED POWER FUNCTION DISTRIBUTION I. E. Okorie 1, A. C. Akpanta 2 and J. Ohakwe 3
MARSHALL-OLKIN EXTENDED POWER FUNCTION DISTRIBUTION I. E. Okorie 1, A. C. Akpanta 2 and J. Ohakwe 3 1 School of Mathematics, University of Manchester, Manchester M13 9PL, UK 2 Department of Statistics,
More informationTHE MODIFIED EXPONENTIAL DISTRIBUTION WITH APPLICATIONS. Department of Statistics, Malayer University, Iran
Pak. J. Statist. 2017 Vol. 33(5), 383-398 THE MODIFIED EXPONENTIAL DISTRIBUTION WITH APPLICATIONS Mahdi Rasekhi 1, Morad Alizadeh 2, Emrah Altun 3, G.G. Hamedani 4 Ahmed Z. Afify 5 and Munir Ahmad 6 1
More informationPlotting data is one method for selecting a probability distribution. The following
Advanced Analytical Models: Over 800 Models and 300 Applications from the Basel II Accord to Wall Street and Beyond By Johnathan Mun Copyright 008 by Johnathan Mun APPENDIX C Understanding and Choosing
More informationBy Godase, Shirke, Kashid. Published: 26 April 2017
Electronic Journal of Applied Statistical Analysis EJASA, Electron. J. App. Stat. Anal. http://siba-ese.unisalento.it/index.php/ejasa/index e-issn: 2070-5948 DOI: 10.1285/i20705948v10n1p29 Tolerance intervals
More informationTHE ODD LINDLEY BURR XII DISTRIBUTION WITH APPLICATIONS
Pak. J. Statist. 2018 Vol. 34(1), 15-32 THE ODD LINDLEY BURR XII DISTRIBUTION WITH APPLICATIONS T.H.M. Abouelmagd 1&3, Saeed Al-mualim 1&2, Ahmed Z. Afify 3 Munir Ahmad 4 and Hazem Al-Mofleh 5 1 Management
More informationEstimation of the Bivariate Generalized. Lomax Distribution Parameters. Based on Censored Samples
Int. J. Contemp. Math. Sciences, Vol. 9, 2014, no. 6, 257-267 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2014.4329 Estimation of the Bivariate Generalized Lomax Distribution Parameters
More informationA Study of Five Parameter Type I Generalized Half Logistic Distribution
Pure and Applied Mathematics Journal 2017; 6(6) 177-181 http//www.sciencepublishinggroup.com/j/pamj doi 10.11648/j.pamj.20170606.14 ISSN 2326-9790 (Print); ISSN 2326-9812 (nline) A Study of Five Parameter
More informationEstimation of Stress-Strength Reliability for Kumaraswamy Exponential Distribution Based on Upper Record Values
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 2, 59-71 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.7210 Estimation of Stress-Strength Reliability for
More informationAlpha-Skew-Logistic Distribution
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 9-765X Volume 0, Issue Ver VI (Jul-Aug 0), PP 6-6 Alpha-Sew-Logistic Distribution Partha Jyoti Haaria a and Subrata Charaborty b a Department
More informationThe Exponentiated Weibull-Power Function Distribution
Journal of Data Science 16(2017), 589-614 The Exponentiated Weibull-Power Function Distribution Amal S. Hassan 1, Salwa M. Assar 2 1 Department of Mathematical Statistics, Cairo University, Egypt. 2 Department
More informationThe Burr X-Exponential Distribution: Theory and Applications
Proceedings of the World Congress on Engineering 7 Vol I WCE 7, July 5-7, 7, London, U.K. The Burr X- Distribution: Theory Applications Pelumi E. Oguntunde, Member, IAENG, Adebowale O. Adejumo, Enahoro
More informationGeneralized Transmuted -Generalized Rayleigh Its Properties And Application
Journal of Experimental Research December 018, Vol 6 No 4 Email: editorinchief.erjournal@gmail.com editorialsecretary.erjournal@gmail.com Received: 10th April, 018 Accepted for Publication: 0th Nov, 018
More informationAnalysis of Hermite s equation governing the motion of damped pendulum with small displacement
Vol. 10(12), pp. 364-370, 30 June, 2015 DOI: 10.5897/IJPS2015.4364 Article Number: 9A709F454056 ISSN 1992-1950 Copyright 2015 Author(s) retain the copyright of this article http://www.academicjournals.org/ijps
More informationNew Flexible Weibull Distribution
ISSN (Print) : 232 3765 (An ISO 3297: 27 Certified Organiation) Vol. 6, Issue 5, May 217 New Flexible Weibull Distribution Zubair Ahmad 1* and Zawar Hussain 2 Research Scholar, Department of Statistics,
More informationTruncated Weibull-G More Flexible and More Reliable than Beta-G Distribution
International Journal of Statistics and Probability; Vol. 6 No. 5; September 217 ISSN 1927-732 E-ISSN 1927-74 Published by Canadian Center of Science and Education Truncated Weibull-G More Flexible and
More informationThe modied beta Weibull distribution
Hacettepe Journal of Mathematics and Statistics Volume 44 6 25, 553 568 The modied beta Weibull distribution Muhammad Nauman Khan Abstract A new ve-parameter model called the modied beta Weibull probability
More informationG.J.B.B., VOL.5 (1) 2016:
ON THE MAXIMUM LIKELIHOOD, BAYES AND EMPIRICAL BAYES ESTIMATION FOR THE SHAPE PARAMETER, RELIABILITY AND FAILURE RATE FUNCTIONS OF KUMARASWAMY DISTRIBUTION Nadia H. Al-Noor & Sudad K. Ibraheem College
More informationTransmuted Pareto distribution
ProbStat Forum, Volume 7, January 214, Pages 1 11 ISSN 974-3235 ProbStat Forum is an e-journal For details please visit wwwprobstatorgin Transmuted Pareto distribution Faton Merovci a, Llukan Puka b a
More informationOn a Generalization of Weibull Distribution and Its Applications
International Journal of Statistics and Applications 26, 6(3): 68-76 DOI:.5923/j.statistics.2663. On a Generalization of Weibull Distribution and Its Applications M. Girish Babu Department of Statistics,
More informationKybernetika. Hamzeh Torabi; Narges Montazeri Hedesh The gamma-uniform distribution and its applications. Terms of use:
Kybernetika Hamzeh Torabi; Narges Montazeri Hedesh The gamma-uniform distribution and its applications Kybernetika, Vol. 48 (202), No., 6--30 Persistent URL: http://dml.cz/dmlcz/4206 Terms of use: Institute
More informationEstimation of Mixed Exponentiated Weibull Parameters in Life Testing
International Mathematical Forum, Vol., 6, no. 6, 769-78 HIKARI Ltd, www.m-hikari.com http://d.doi.org/.988/imf.6.6445 Estimation of Mied Eponentiated Weibull Parameters in Life Testing A. M. Abd-Elrahman
More informationPOWER GENERALIZED WEIBULL DISTRIBUTION BASED ON ORDER STATISTICS
Journal of Statistical Research 27, Vol. 5, No., pp. 6-78 ISSN 256-422 X POWER GENERALIZED WEIBULL DISTRIBUTION BASED ON ORDER STATISTICS DEVENDRA KUMAR Department of Statistics, Central University of
More informationSome recent developments in probability distributions
Proeedings 59th ISI World Statistis Congress, 25-30 August 2013, Hong Kong (Session STS084) p.2873 Some reent developments in probability distributions Felix Famoye *1, Carl Lee 1, and Ayman Alzaatreh
More informationTransmuted New Weibull-Pareto Distribution and its Applications
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 932-9466 Vol. 3, Issue (June 28), pp. 3-46 Applications and Applied Mathematics: An International Journal (AAM) Transmuted New Weibull-Pareto Distribution
More informationInternational Journal of Scientific & Engineering Research, Volume 6, Issue 2, February-2015 ISSN
1686 On Some Generalised Transmuted Distributions Kishore K. Das Luku Deka Barman Department of Statistics Gauhati University Abstract In this paper a generalized form of the transmuted distributions has
More informationPLEASE SCROLL DOWN FOR ARTICLE
This article was downloaded by: [Kundu, Debasis] On: 4 November 2009 Access details: Access Details: [subscription number 9655482] Publisher Taylor & Francis Informa Ltd Registered in England and Wales
More informationBurr Type X Distribution: Revisited
Burr Type X Distribution: Revisited Mohammad Z. Raqab 1 Debasis Kundu Abstract In this paper, we consider the two-parameter Burr-Type X distribution. We observe several interesting properties of this distribution.
More informationTail Approximation of the Skew-Normal by the Skew-Normal Laplace: Application to Owen s T Function and the Bivariate Normal Distribution
Journal of Statistical and Econometric ethods vol. no. 3 - ISS: 5-557 print version 5-565online Scienpress Ltd 3 Tail Approimation of the Skew-ormal by the Skew-ormal Laplace: Application to Owen s T Function
More informationStep-Stress Models and Associated Inference
Department of Mathematics & Statistics Indian Institute of Technology Kanpur August 19, 2014 Outline Accelerated Life Test 1 Accelerated Life Test 2 3 4 5 6 7 Outline Accelerated Life Test 1 Accelerated
More informationThe Kumaraswamy-G Poisson Family of Distributions
Journal of Statistical Theory and Applications, Vol. 14, No. 3 (September 2015), 222-239 The Kumaraswamy-G Poisson Family of Distributions Manoel Wallace A. Ramos 1,, Pedro Rafael D. Marinho 2, Gauss M.
More informationExponential modified discrete Lindley distribution
Yilmaz et al. SpringerPlus 6 5:66 DOI.86/s464-6-33- RESEARCH Open Access Eponential modified discrete Lindley distribution Mehmet Yilmaz *, Monireh Hameldarbandi and Sibel Aci Kemaloglu *Correspondence:
More informationA new method for generating families of continuous distributions
METRON (2013) 71:63 79 DOI 10.1007/s40300-013-0007-y A new method for generating families of continuous distributions Ayman Alzaatreh Carl Lee Felix Famoye Received: 9 March 2011 / Accepted: 16 February
More informationReliability Engineering I
Happiness is taking the reliability final exam. Reliability Engineering I ENM/MSC 565 Review for the Final Exam Vital Statistics What R&M concepts covered in the course When Monday April 29 from 4:30 6:00
More informationJournal of Environmental Statistics
jes Journal of Environmental Statistics February 2010, Volume 1, Issue 3. http://www.jenvstat.org Exponentiated Gumbel Distribution for Estimation of Return Levels of Significant Wave Height Klara Persson
More informationThe Generalized Odd Gamma-G Family of Distributions: Properties and Applications
Austrian Journal of Statistics February 218, Volume 47, 69 89. AJS http://www.ajs.or.at/ doi:1.17713/ajs.v47i2.58 The Generalized Odd Gamma-G Family of Distributions: Properties and Applications B. Hosseini
More informationOn Weighted Exponential Distribution and its Length Biased Version
On Weighted Exponential Distribution and its Length Biased Version Suchismita Das 1 and Debasis Kundu 2 Abstract In this paper we consider the weighted exponential distribution proposed by Gupta and Kundu
More informationA New Flexible Version of the Lomax Distribution with Applications
International Journal of Statistics and Probability; Vol 7, No 5; September 2018 ISSN 1927-7032 E-ISSN 1927-7040 Published by Canadian Center of Science and Education A New Flexible Version of the Lomax
More informationThe Weibull-Geometric Distribution
Journal of Statistical Computation & Simulation Vol., No., December 28, 1 14 The Weibull-Geometric Distribution Wagner Barreto-Souza a, Alice Lemos de Morais a and Gauss M. Cordeiro b a Departamento de
More informationChapter 2. Discrete Distributions
Chapter. Discrete Distributions Objectives ˆ Basic Concepts & Epectations ˆ Binomial, Poisson, Geometric, Negative Binomial, and Hypergeometric Distributions ˆ Introduction to the Maimum Likelihood Estimation
More informationA Mixture of Modified Inverse Weibull Distribution
J. Stat. Appl. Pro. Lett., No. 2, 3-46 (204) 3 Journal of Statistics Applications & Probability Letters An International Journal http://dx.doi.org/0.2785/jsapl/00203 A Mixture of Modified Inverse Weibull
More informationSize Biased Lindley Distribution Properties and its Applications: A Special Case of Weighted Distribution
Size Biased Lindley Distribution Properties and its Applications: A Special Case of Weighted Distribution Arooj Ayesha* Department of Mathematics and Statistics, University of agriculture Faisalabad, Pakistan
More informationON THE TRUNCATED COMPOSITE WEIBULL-PARETO MODEL
ON THE TRUNCATED COMPOSITE WEIBULL-PARETO MODEL SANDRA TEODORESCU and EUGENIA PANAITESCU The composite Weibull-Pareto model 2] was introduced as an alternative to the composite Lognormal-Pareto ] used
More informationReview Quiz. 1. Prove that in a one-dimensional canonical exponential family, the complete and sufficient statistic achieves the
Review Quiz 1. Prove that in a one-dimensional canonical exponential family, the complete and sufficient statistic achieves the Cramér Rao lower bound (CRLB). That is, if where { } and are scalars, then
More informationEconomic Reliability Test Plans using the Generalized Exponential Distribution
ISSN 684-843 Journal of Statistics Volume 4, 27, pp. 53-6 Economic Reliability Test Plans using the Generalized Exponential Distribution Muhammad Aslam and Muhammad Qaisar Shahbaz 2 Abstract Economic Reliability
More informationWeighted Marshall-Olkin Bivariate Exponential Distribution
Weighted Marshall-Olkin Bivariate Exponential Distribution Ahad Jamalizadeh & Debasis Kundu Abstract Recently Gupta and Kundu [9] introduced a new class of weighted exponential distributions, and it can
More informationThe Exponentiated Generalized Standardized Half-logistic Distribution
International Journal of Statistics and Probability; Vol. 6, No. 3; May 27 ISSN 927-732 E-ISSN 927-74 Published by Canadian Center of Science and Education The Eponentiated Generalized Standardized Half-logistic
More informationWeighted Exponential Distribution and Process
Weighted Exponential Distribution and Process Jilesh V Some generalizations of exponential distribution and related time series models Thesis. Department of Statistics, University of Calicut, 200 Chapter
More informationTHE FIVE PARAMETER LINDLEY DISTRIBUTION. Dept. of Statistics and Operations Research, King Saud University Saudi Arabia,
Pak. J. Statist. 2015 Vol. 31(4), 363-384 THE FIVE PARAMETER LINDLEY DISTRIBUTION Abdulhakim Al-Babtain 1, Ahmed M. Eid 2, A-Hadi N. Ahmed 3 and Faton Merovci 4 1 Dept. of Statistics and Operations Research,
More informationA Class of Weighted Weibull Distributions and Its Properties. Mervat Mahdy Ramadan [a],*
Studies in Mathematical Sciences Vol. 6, No. 1, 2013, pp. [35 45] DOI: 10.3968/j.sms.1923845220130601.1065 ISSN 1923-8444 [Print] ISSN 1923-8452 [Online] www.cscanada.net www.cscanada.org A Class of Weighted
More informationTHE BIVARIATE F 3 -BETA DISTRIBUTION. Saralees Nadarajah. 1. Introduction
Commun. Korean Math. Soc. 21 2006, No. 2, pp. 363 374 THE IVARIATE F 3 -ETA DISTRIUTION Saralees Nadarajah Abstract. A new bivariate beta distribution based on the Appell function of the third kind is
More informationIntroduction of Shape/Skewness Parameter(s) in a Probability Distribution
Journal of Probability and Statistical Science 7(2), 153-171, Aug. 2009 Introduction of Shape/Skewness Parameter(s) in a Probability Distribution Rameshwar D. Gupta University of New Brunswick Debasis
More informationThe Kumaraswamy-geometric distribution
Akinsete et al. Journal of Statistical Distributions and Applications 2014 1:17 RESEARCH Open Access The Kumaraswamy-geometric distribution Alfred Akinsete 1* FelixFamoye 2 and Carl Lee 2 *Correspondence:
More informationCharacterization of the Skew-Normal Distribution Via Order Statistics and Record Values
International Journal of Statistics and Probabilit; Vol. 4, No. 1; 2015 ISSN 1927-7032 E-ISSN 1927-7040 Published b Canadian Center of Science and Education Characterization of the Sew-Normal Distribution
More informationProbability and Stochastic Processes
Probability and Stochastic Processes A Friendly Introduction Electrical and Computer Engineers Third Edition Roy D. Yates Rutgers, The State University of New Jersey David J. Goodman New York University
More informationAn alternative two-parameter gamma generated family of distributions: properties and applications
Hacettepe Journal of Mathematics and Statistics Volume 47 1 218, 145 173 An alternative two-parameter gamma generated family of distributions: properties and applications Gauss M Cordeiro, Saralees Nadarajah,
More informationThe Beta-Gompertz Distribution
Revista Colombiana de Estadística Junio 2014, volumen 37, no. 1, pp. 139 a 156 The Beta-Gompertz Distribution La distribución Beta-Gompertz Ali Akbar Jafari 1,a, Saeid Tahmasebi 2,b, Morad Alizadeh 3,c
More informationA GENERALIZED CLASS OF EXPONENTIATED MODI ED WEIBULL DISTRIBUTION WITH APPLICATIONS
Journal of Data Science 14(2016), 585-614 A GENERALIZED CLASS OF EXPONENTIATED MODI ED WEIBULL DISTRIBUTION WITH APPLICATIONS Shusen Pu 1 ; Broderick O. Oluyede 2, Yuqi Qiu 3 and Daniel Linder 4 Abstract:
More informationProbability Distribution
Probability Distribution Prof. (Dr.) Rajib Kumar Bhattacharjya Indian Institute of Technology Guwahati Guwahati, Assam Email: rkbc@iitg.ernet.in Web: www.iitg.ernet.in/rkbc Visiting Faculty NIT Meghalaya
More informationBivariate Weibull-power series class of distributions
Bivariate Weibull-power series class of distributions Saralees Nadarajah and Rasool Roozegar EM algorithm, Maximum likelihood estimation, Power series distri- Keywords: bution. Abstract We point out that
More informationThe Kumaraswamy Gompertz distribution
Journal of Data Science 13(2015), 241-260 The Kumaraswamy Gompertz distribution Raquel C. da Silva a, Jeniffer J. D. Sanchez b, F abio P. Lima c, Gauss M. Cordeiro d Departamento de Estat ıstica, Universidade
More informationDiscriminating Between the Bivariate Generalized Exponential and Bivariate Weibull Distributions
Discriminating Between the Bivariate Generalized Exponential and Bivariate Weibull Distributions Arabin Kumar Dey & Debasis Kundu Abstract Recently Kundu and Gupta ( Bivariate generalized exponential distribution,
More informationThe transmuted geometric-quadratic hazard rate distribution: development, properties, characterizations and applications
Bhatti et al. Journal of Statistical Distributions and Applications (018) 5:4 https://doi.org/10.1186/s40488-018-0085-8 RESEARCH The transmuted geometric-quadratic hazard rate distribution: development,
More informationThe Geometric Inverse Burr Distribution: Model, Properties and Simulation
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 11, Issue 2 Ver. I (Mar - Apr. 2015), PP 83-93 www.iosrjournals.org The Geometric Inverse Burr Distribution: Model, Properties
More informationMath Honors Calculus I Final Examination, Fall Semester, 2013
Math 2 - Honors Calculus I Final Eamination, Fall Semester, 2 Time Allowed: 2.5 Hours Total Marks:. (2 Marks) Find the following: ( (a) 2 ) sin 2. (b) + (ln 2)/(+ln ). (c) The 2-th Taylor polynomial centered
More informationTL- MOMENTS AND L-MOMENTS ESTIMATION FOR THE TRANSMUTED WEIBULL DISTRIBUTION
Journal of Reliability and Statistical Studies; ISSN (Print): 0974-804, (Online): 9-5666 Vol 0, Issue (07): 7-36 TL- MOMENTS AND L-MOMENTS ESTIMATION FOR THE TRANSMUTED WEIBULL DISTRIBUTION Ashok Kumar
More informationTail Properties and Asymptotic Expansions for the Maximum of Logarithmic Skew-Normal Distribution
Tail Properties and Asymptotic Epansions for the Maimum of Logarithmic Skew-Normal Distribution Xin Liao, Zuoiang Peng & Saralees Nadarajah First version: 8 December Research Report No. 4,, Probability
More information